2,402 research outputs found
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
C1-continuous space-time discretization based on Hamilton's law of varying action
We develop a class of C1-continuous time integration methods that are
applicable to conservative problems in elastodynamics. These methods are based
on Hamilton's law of varying action. From the action of the continuous system
we derive a spatially and temporally weak form of the governing equilibrium
equations. This expression is first discretized in space, considering standard
finite elements. The resulting system is then discretized in time,
approximating the displacement by piecewise cubic Hermite shape functions.
Within the time domain we thus achieve C1-continuity for the displacement field
and C0-continuity for the velocity field. From the discrete virtual action we
finally construct a class of one-step schemes. These methods are examined both
analytically and numerically. Here, we study both linear and nonlinear systems
as well as inherently continuous and discrete structures. In the numerical
examples we focus on one-dimensional applications. The provided theory,
however, is general and valid also for problems in 2D or 3D. We show that the
most favorable candidate -- denoted as p2-scheme -- converges with order four.
Thus, especially if high accuracy of the numerical solution is required, this
scheme can be more efficient than methods of lower order. It further exhibits,
for linear simple problems, properties similar to variational integrators, such
as symplecticity. While it remains to be investigated whether symplecticity
holds for arbitrary systems, all our numerical results show an excellent
long-term energy behavior.Comment: slightly condensed the manuscript, added references, numerical
results unchange
Tracing planet-induced structures in circumstellar disks using molecular lines
Circumstellar disks are considered to be the birthplace of planets. Specific
structures like spiral arms, gaps, and cavities are characteristic indicators
of planet-disk interaction. Investigating these structures can provide insights
into the growth of protoplanets and the physical properties of the disk. We
investigate the feasibility of using molecular lines to trace planet-induced
structures in circumstellar disks. Based on 3D hydrodynamic simulations of
planet-disk interactions, we perform self-consistent temperature calculations
and produce N-LTE molecular line velocity-channel maps and spectra of these
disks using our new N-LTE line radiative transfer code Mol3D. Subsequently, we
simulate ALMA observations using the CASA simulator. We consider two nearly
face-on inclinations, 5 disk masses, 7 disk radii, and 2 different typical
pre-main-sequence host stars (T Tauri, Herbig Ae). We calculate up to 141
individual velocity-channel maps for five molecules/isotopoloques in a total of
32 rotational transitions to investigate the frequency dependence of the
structures indicated above. We find that the majority of protoplanetary disks
in our parameter space could be detected in the molecular lines considered.
However, unlike the continuum case, gap detection is not straightforward in
lines. For example, gaps are not seen in symmetric rings but are masked by the
pattern caused by the global (Keplerian) velocity field. We identify specific
regions in the velocity-channel maps that are characteristic of planet-induced
structures. Simulations of high angular resolution molecular line observations
demonstrate the potential of ALMA to provide complementary information about
the planet-disk interaction as compared to continuum observations. In
particular, the detection of planet-induced gaps is possible under certain
conditions.(abridged)Comment: 19 pages, 19 figures, accepted for publication in A&
Improving optimal control of grid-connected lithium-ion batteries through more accurate battery and degradation modelling
The increased deployment of intermittent renewable energy generators opens up
opportunities for grid-connected energy storage. Batteries offer significant
flexibility but are relatively expensive at present. Battery lifetime is a key
factor in the business case, and it depends on usage, but most techno-economic
analyses do not account for this. For the first time, this paper quantifies the
annual benefits of grid-connected batteries including realistic physical
dynamics and nonlinear electrochemical degradation. Three lithium-ion battery
models of increasing realism are formulated, and the predicted degradation of
each is compared with a large-scale experimental degradation data set
(Mat4Bat). A respective improvement in RMS capacity prediction error from 11\%
to 5\% is found by increasing the model accuracy. The three models are then
used within an optimal control algorithm to perform price arbitrage over one
year, including degradation. Results show that the revenue can be increased
substantially while degradation can be reduced by using more realistic models.
The estimated best case profit using a sophisticated model is a 175%
improvement compared with the simplest model. This illustrates that using a
simplistic battery model in a techno-economic assessment of grid-connected
batteries might substantially underestimate the business case and lead to
erroneous conclusions
State Space Formulas for Coprime Factorization
In this paper we will give a uniform approach to the derivation of state space formulas of coprime factorizations, of different types, for rational matrix functions
Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids
In the past twenty years, shear-banding flows have been probed by various
techniques, such as rheometry, velocimetry and flow birefringence. In micellar
solutions, many of the data collected exhibit unexplained spatio-temporal
fluctuations. Recently, it has been suggested that those fluctuations originate
from a purely elastic instability of the flow. In cylindrical Couette geometry,
the instability is reminiscent of the Taylor-like instability observed in
viscoelastic polymer solutions. In this letter, we describe how the criterion
for purely elastic Taylor-Couette instability should be adapted to
shear-banding flows. We derive three categories of shear-banding flows with
curved streamlines, depending on their stability.Comment: 6 pages, 3 figure
- âŠ